Algebraic Solution for $(y - z)^2$
We are given the equations:
- $ (y + z) = 8 $
- $ yz = 6 $
We need to find the value of $ (y - z)^2 $.
Applying Algebraic Identity
We use the algebraic identity that relates $ (y + z)^2 $, $ (y - z)^2 $, and $ yz $: $ (y - z)^2 = (y + z)^2 - 4yz $
Calculation
Substitute the given values into the identity:
$ (y - z)^2 = (8)^2 - 4(6) $
$ (y - z)^2 = 64 - 24 $
$ (y - z)^2 = 40 $
Thus, the value of $ (y - z)^2 $ is 40.
Similar Questions
- If $a + b + c = 10$ and $ab + bc + ca = 31$, find the value of $a^2 + b^2 + c^2$
If $a + b + c = 0$, then find the value of $\frac{(a^2+b^2+c^2)^2}{a^2b^2+b^2c^2+c^2a^2}$
- If $x^4 + \frac{1}{x^4} = 322$, then $x^3 - \frac{1}{x^3} = ?$
- What is the value of the following expression:
$(1 + x)(1 + x^2)(1 + x^4)(1 + x^8)(1 - x)$ - If $a + b + c = 17$, $abc = 168$, and $ab + bc + ca = 94$, then $a^3 + b^3 + c^3 = ?$
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- If $(x + \frac{1}{x}) = 7$, then $(x - \frac{1}{x})$ is equal to:
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Important Questions from Identities
The coefficient of y in the expansion of (2y – 5) 3, is:
If x + y = 2 and \(\frac{1}{x}+\frac{1}{y}=\frac{18}{5}\) , then the value of (x 3+ y 3) is:
If x - y = 11 and \(\rm \frac{1}{x} - \frac{1}{y} = \frac{11}{24}\) then the value of x 3 - y 3 + x 2y 2 ?
If 2x 2- 8x - 1 = 0, then what is the value of \(\rm 8x^3 - \frac{1}{x^3}\) ?
If \(\rm x+ \frac{1}{x} = 4,\) then the value of \(\rm x^5 + \frac{1}{x^5}\) is:
